Chapter 2.4, Problem 3P

Explanation of Solution

Determining the dependency of the given sets of vectors:

Consider the given sets of vectors,

$V=\{[21],[12]\}$

A matrix A is formed as given below; whose rows are the above given vectors:

$A=\left[\begin{array}{l}21\\ 12\end{array}\right]$

The Gauss-Jordan method is applied to find the dependency of the above given sets of vectors.

Replace row 1 by $\frac{1}{2}(row1)$, then the following matrix is obtained,

$\left[\begin{array}{l}1\frac{1}{2}\\ 12\end{array}\right]$

Replace row 2 by (row 2 – row 1), then the following matrix is obtained,

$\left[\begin{array}{l}1\frac{1}{2}\\ 0\frac{3}{2}\end{array}\right]$

Replace row 2 by $\frac{2}{3}$